<h3>Given</h3>
- a cone of height 0.4 m and diameter 0.3 m
- filling at the rate 0.004 m³/s
- fill height of 0.2 m at the time of interest
<h3>Find</h3>
- the rate of change of fill height at the time of interest
<h3>Solution</h3>
The cone is filled to half its depth at the time of interest, so the surface area of the filled portion will be (1/2)² times the surface area of the top of the cone. The filled portion has an area of
... A = (1/4)(π/4)d² = (π/16)(0.3 m)² = 0.09π/16 m²
This area multiplied by the rate of change of fill height (dh/dt) will give the rate of change of volume.
... (0.09π/16 m²)×dh/dt = dV/dt = 0.004 m³/s
Dividing by the coefficient of dh/dt, we get
... dh/dt = 0.004·16/(0.09π) m/s
... dh/dt = 32/(45π) m/s ≈ 0.22635 m/s
_____
You can also write an equation for the filled volume in terms of the filled height, then differentiate and solve for dh/dt. When you do, you find the relation between rates of change of height and area are as described above. We have taken a "shortcut" based on the knowledge gained from solving it this way. (No arithmetic operations are saved. We only avoid the process of taking the derivative.)
Note that the cone dimensions mean the radius is 3/8 of the height.
V = (1/3)πr²h = (1/3)π(3/8·h)²·h = 3π/64·h³
dV/dt = 9π/64·h²·dh/dt
.004 = 9π/64·0.2²·dh/dt . . . substitute the given values
dh/dt = .004·64/(.04·9·π) = 32/(45π)
Answer:
c>-13/10
Step-by-step explanation:
55c+13<75c+39
55c+13-75c<39
-20c+13<39
-20c<39-13
-20c<26
c>26/-20
c>-13/10
Answer:
8,246,160
Step-by-step explanation:
Population density
= people/area
Given
Population density of New York = 17,620 and
Area = 468 square mile
Therefore,
17620 = people /468
Cross multiply
People = 17620 x 468
= 8246160
There are 8,246,160 people in New York
we know that
if ∠UVW and ∠XYZ are complementary angles
then
∠UVW + ∠XYZ=90°
∠UVW=x-10
∠XYZ=4x-10
substitute the values
(x-10)°+(4x-10)°=90°
Solve for x
5x-20=90
5x=90+20
5x=110
x=22°
∠UVW=x-10=22-10=12°
∠XYZ=4x-10=4*22-10=78°
therefore
<u>the answer is</u>
x=22°
∠UVW=12°
∠XYZ=78°
Answer:
I think it is 5 units
Step-by-step explanation:
Lemme know if you need more help! :))
